Tetragonal Domains Research Articles

Mapping domain structures near a grain boundary in a lead zirconate titanate ferroelectric film using X-ray nanodiffraction

The effect of an electric field on local domain structure near a 24° tilt grain boundary in a 200 nm-thick Pb(Zr0.2Ti0.8)O3 bi-crystal ferroelectric film was probed using synchrotron nanodiffraction. The bi-crystal film was grown epitaxially on SrRuO3-coated (001) SrTiO3 24° tilt bi-crystal substrates. From the nanodiffraction data, real-space maps of the ferroelectric domain structure around the grain boundary prior to and during application of a 200 kV cm−1 electric field were reconstructed. In the vicinity of the tilt grain boundary, the distributions of densities of c-type tetragonal domains with the c axis aligned with the film normal were calculated on the basis of diffracted intensity ratios of c- and a-type domains and reference powder diffraction data. Diffracted intensity was averaged along the grain boundary, and it was shown that the density of c-type tetragonal domains dropped to ∼50% of that of the bulk of the film over a range ±150 nm from the grain boundary. This work complements previous results acquired by band excitation piezoresponse force microscopy, suggesting that reduced nonlinear piezoelectric response around grain boundaries may be related to the change in domain structure, as well as to the possibility of increased pinning of domain wall motion. The implications of the results and analysis in terms of understanding the role of grain boundaries in affecting the nonlinear piezoelectric and dielectric responses of ferroelectric materials are discussed.

Lattice match between coexisting cubic and tetragonal phases in PMN-PT at the phase transition

(1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) perovskite-like solid solutions are recognized for their outstanding electromechanical properties, which are of technological importance. However, some significant aspects of the crystal structures and domain assemblages in this system and the role of these characteristics in defining the functional performance of PMN-PT remain uncertain. Here, we used synchrotron x-ray diffraction to investigate the phase transition linking the paraelectric (cubic) and ferroelectric (tetragonal) phases in a single crystal of 0.65PMN-0.35PT. We analyzed the evolution of reciprocal-space maps across this transition. These maps were collected using small temperature step (1 K) and a high reciprocal-space resolution to reveal changes in the splitting of Bragg peaks caused by the formation of ferroelastic domains in the low-symmetry phase. Our results uncovered a two-phase state, cubic plus tetragonal phases, which exists over a narrow temperature range of only ≈4 K and exhibits a thermal hysteresis of ≈1.8 K. Remarkably, within this state, the lattice parameter of the cubic phase, aC, matches the orientational average of the lattice parameters for the tetragonal polymorph, 23aT+13cT. We discuss the implications of this matching, highlighting the possibility of it being realized by the formation of an assemblage of tetragonal twin domains separated from the cubic phase by a strain-free {110} boundary, as in the “adaptive phase” but without domain miniaturization.

Strain-affected ferroelastic domain walls in RbMnFe charge-transfer materials undergoing collective Jahn-Teller distortion.

Many rubidium manganese hexacyanoferrate materials, with the general formula Rb x Mn[Fe(CN)6](x+2)/3·zH2O, exhibit diverse charge-transfer-based functionalities due to the bistability between a high temperature MnII(S = 5/2)FeIII(S = 1/2) cubic phase and a low-temperature MnIII(S = 2)FeII(S = 0) tetragonal phase. The collective Jahn-Teller distortion on the Mn sites is responsible for the cubic-to-tetragonal ferroelastic phase transition, which is associated with the appearance of ferroelastic domains. In this study, we use X-ray diffraction to reveal the coexistence of 3 types of ferroelastic tetragonal domains and estimate the spatial extension of the strain around the domain walls, which represents about 30% of the volume of the crystal.

Achieving large strain and excellent temperature stability in PT-PZ-LST piezoelectric ceramics

Lead-based piezoelectric ceramics are the preferred material for commercial piezoelectric ceramic actuators due to their high performance and irreplaceability. However, the operating temperature (<100 °C) and strain (0.1 %∼0.2 %) of lead-based piezoelectric ceramics are still limited. Achieving large strain in a wide temperature range remains challenging. In this paper, a new strategy is proposed to effectively increase the strain value of lead-based piezoelectric ceramics through domain engineering. The new xPbTiO3-(0.97-x)PbZrO3-0.03(La0.1Sr0.80.1)TiO2.95 (xPT-PZ-LST) ternary piezoelectric ceramic system reaches a strain value as high as 0.5 % and exhibits extremely high temperature stability (13 %) in the range of 25–230 °C. By fine-tuning the content of PT components, the average length and width of a typical tetragonal domain are transformed from 800 nm to 80 nm (long and thin) to 300 nm and 200 nm (short and wide), relatively. From the experimental results of PFM and Rayleigh analysis, the high strain can be attributed to the synergistic effect of the reduced coercive field (Ec), enhanced micro-region response, and regulated domain morphology, which ensures that high intrinsic and extrinsic contribution can be achieved at the same time. In this paper, a new strain regulation method is provided for lead-based piezoelectric ceramics, and a valuable large strain material is obtained via domain engineering.

Domain engineering in ferromagnetic morphotropic phase boundary with enhanced and non-hysteretic magnetostriction: A phase-field simulation

Giant and non-hysteretic magnetostriction is critical for magneto-mechanical applications, such as transducers, sensors, and actuators. In this work, the introduction of domain engineering into the single crystals near the ferromagnetic morphotropic phase boundary (MPB) is achieved through phase-field simulation, with the aim of exerting control over domain configuration and magnetostriction. It is found that intermediate external magnetic fields applied along non-easy magnetic axes during the nucleation stage can significantly affect the subsequent domain growth and evolution kinetics. The simulations reveal a domain wall broadening mechanism to explain the significantly improved non-hysteretic magnetoelastic responses observed in engineered tetragonal crystals. Our simulation results additionally demonstrate a discernible correlation between the domain wall densities and external fields in the engineered tetragonal domain. This research provides a potential pathway for the advancement of giant and non-hysteretic magnetostrictive material designs.

Second Harmonic Generation Studies of Interfacial Strain Engineering in BaZr0.2Ti0.8O3

AbstractFilm ferroelectrics demonstrate large breakdown strength, high energy density, and many unique phenomena not found in bulk materials. In this investigation, a rhombohedral BaZr0.2Ti0.8O3 (BZT) solid solution and various film‐substrate misfit strains are utilized to optimize the energy storage performance of ferroelectric thick films. Optical second harmonic generation is applied in both reflection and transmission geometries to reveal the renovation of entangled rhombohedral and tetragonal phases in the BZT films under compressive misfit strains. It is shown that the interfacial strain between the BZT film and substrate introduces the tetragonal domains. The competition between the tetragonal and rhombohedral phases creates the self‐assembled, anisotropically strained morphotropic structures to effectively accommodate the elastic and electrical stress fields through inside the thick BZT film. The BZT films demonstrate exceptional energy storage performance because of the adaptable nano‐domain structure within the bulk of the BZT films and may be engineered to optimize the superior performance of BZT films in energy storage.

Quantification of polarization distribution from polarizing light microscopy images of ferroelectric single crystals

Qualification of polarization can be realized either on a macroscopic scale as an average property by P-E hysteresis measurements or on a nano/micro scale by piezoelectric force microscopy, transmission electron microscopy, scanning electron microscopy, and so on. However, visualization and qualification of polarization distribution in the micron to millimeter scale is still a challenge. Polarizing light microscopy (PLM) is often used in the study of ferroelectric domain structures mainly for domain patterns. A phenomenon called “chromatic polarization” has been observed in transparent ferroelectric crystals by using a crossed-PLM system viewed with white light, which contains rich information about local polarization distribution. In this study, an automatic full-angle light intensity detection (AFALID) algorithm combined with colorimetry is developed to analyze the distribution of nonuniform local spontaneous polarization distribution in transparent ferroelectric single crystals. Temperature-dependent spontaneous polarizations from the color analysis for PMN-0.36PT single crystals with single tetragonal domain state are in good coincidence with those extracted from temperature-dependent hysteresis loops and pyroelectric current measurements. We further apply this method to quantify the nonuniform domain distributions with nano-indentations. This non-contact and non-destructive characterization can provide fast and automatic detection of polarization distributions in ferroelectric materials.

Majorana-Weyl cones in ferroelectric superconductors

Topological superconductors are predicted to exhibit outstanding phenomena, including non-Abelian anyon excitations, heat-carrying edge states, and topological nodes in the Bogoliubov spectra. Nonetheless, and despite major experimental efforts, we are still lacking unambiguous signatures of such exotic phenomena. In this context, the recent discovery of coexisting superconductivity and ferroelectricity in lightly doped and ultraclean ${\mathrm{SrTiO}}_{3}$ opens new opportunities. Indeed, a promising route to engineer topological superconductivity is the combination of strong spin-orbit coupling and inversion-symmetry breaking. Here we study a three-dimensional parabolic band minimum with Rashba spin-orbit coupling, whose axis is aligned by the direction of a ferroelectric moment. We show that all of the aforementioned phenomena naturally emerge in this model when a magnetic field is applied. Above a critical Zeeman field, Majorana-Weyl cones emerge regardless of the electronic density. These cones manifest themselves as Majorana arc states appearing on surfaces and tetragonal domain walls. Rotating the magnetic field with respect to the direction of the ferroelectric moment tilts the Majorana-Weyl cones, eventually driving them into the type-II state with Bogoliubov Fermi surfaces. We then consider the consequences of the orbital magnetic field. First, the single vortex is found to be surrounded by a topological halo and is characterized by two Majorana zero modes: one localized in the vortex core and the other on the boundary of the topological halo. Based on a semiclassical argument we show that upon increasing the field above a critical value the halos overlap and eventually percolate through the system, causing a bulk topological transition that always precedes the normal state. Finally, we propose concrete experiments to test our predictions.

Effect of local compositional heterogeneity on the piezoelectric property at ferroelectric morphotropic phase boundary – A phase field study

In this work, the effect of local compositional heterogeneity on the domain structure and piezoelectricity at ferroelectric morphotropic phase boundary (MPB) is studied by phase field simulations. It is found that the local compositional heterogeneity leads to a unique domain structure at MPB, i.e., a mixture of tetragonal, monoclinic and rhombohedral domains. Although polarization rotation occurs for both MPB samples with and without local compositional heterogeneity, the piezoelectric d33 coefficient becomes reduced for the sample with local compositional heterogeneity because polarization rotation becomes more difficult on average. This work unravels the effect of local compositional heterogeneity on the piezoelectric property of ferroelectric MPB.

Efficient Cocatalyst-Free Piezo-Photocatalytic Hydrogen Evolution of Defective BaTiO3–x Nanoparticles from Seawater

Hydrogen is a promising fossil-fuel alternative fuel owing to its environmentally neutral emissions and high energy density. However, the need for purified water and external power are critical hindrances to the implementation of hydrogen production. The present work demonstrates the potential to overcome these shortcomings through piezo-photocatalysis of seawater using defective BaTiO3–x (BTO) nanoparticles. This material was made piezoelectrically active by a straightforward annealing process under different atmospheres, including O2, N2, Ar, or H2, the latter of which caused Ti4+ → Ti(4–x)+ multiple reductions and structural distortions that stabilize piezoelectric tetragonal domains. A suite of experimental techniques was employed to reveal the effects of reduction on the energy band structure. A substantial piezoelectric effect and the presence of self-polarization were confirmed by piezoresponse force microscopy, while simulation work clarified the role of vibrations on band bending deriving from the self-polarization. The hydrogen evolution through photocatalysis, piezocatalysis, and piezo-photocatalysis over the defective BaTiO3–x nanoparticles was characterized with deionized (DI) water, simulated seawater, and natural seawater. A promising HER with a rate of 132.4 μmol/g/h was achieved using DI water through piezo-photocatalysis without a cocatalyst. In contrast, a substantial HER rate of 48.7 μmol/g/h was obtained for natural seawater, despite the deleterious impact of dissolved ions. The present work offers new perspectives for large-scale green H2 production using abundant natural resources with a conventional piezoelectric material that is readily available but still affected by the ions dissolved in seawater.

A combination of large unipolar electrostrain and d33 in a non-ergodic relaxor ferroelectric

One of the important requirements for piezoelectric materials for use as high strain actuators is that they exhibit large unipolar electrostrain with minimum hysteresis. While large unipolar electrostrain &amp;gt;1% is generally achievable in good quality single crystals, most polycrystalline piezoelectric show low values &amp;lt; 0.4%. Unipolar electrostrain 0.5%–0.7% in polycrystalline piezoelectrics has often been reported in Na0.5Bi0.5TiO3-based compositions at the non-ergodic ergodic boundary. Not amenable to poling, such materials exhibit almost nearly zero direct piezoelectric coefficient (d33 ∼ 0 pC/N) and cannot be simultaneously used as a sensor. In this paper, we report a combination of large unipolar electrostrain of ∼0.6% with small strain hysteresis of 25% in a Sn-modified relaxor ferroelectric system PbTiO3–Bi(Ni1/2Zr1/2)O3. It exhibits d33 ∼ 340 pC/N, which is stable up to 130 °C, and large signal converse piezoelectric coefficient d33* ∼ 1200 pm/V. A combination of large d33 and d33* in the same material makes it an important candidate for simultaneous use as a sensor and high strain actuators. X-ray diffraction study in situ with the electric field suggests that large electrostrain with low strain hysteresis in this system is because of the increased reversible switching of the field stabilized tetragonal ferroelastic domains.

Nanoarchitectonics of self-assembled chessboard-like structures by recurrent phase separation and coalescence of nano domains in CoFeMn oxide

Self-assembled chessboard-like (CB-like) nanostructures in oxides are potential candidate materials for high density memory and energy storage devices. The evolution of CB-like nanostructures has been studied by combining transmission electron microscopy and 3D atom probe tomography in spinel-forming CoFeMn oxide. CB-like nanostructures evolve through a complex process of twinning, subdomain formation through recurrent pseudo-spinodal decomposition and domain coalescence along specific crystallographic axes. It initiates with the cross-penetration of compound deformation twins with subtle chemical composition separation between different domains, which ultimately results in the polymorphic transformation of cubic and tetragonal phases. The requirement of interfacial strain minimization leads to the formation of two tetragonal and two cubic spinel domains of different compositions which are rotationally orientated. In the CB-like nanostructure, cubic and tetragonal domains are connected along 〈022〉 directions. Cubic with cubic domains, and tetragonal with tetragonal domains, are connected along 〈040〉 or 〈004〉 directions. Recurring pseudo-spinodal decomposition within the CB-like domains leads to the formation of finer CB-like nanodomains. The formation of cuboid shaped domains of the cubic and tetragonal phases to rod shape morphology with four {220} and two {001} faces can give rise to 2D CB-like nanostructures. Combined transmission electron microscopy and atom probe tomography analysis indicates that CB-like nanostructures can also form in 3D, and a new model for this has been proposed based on the octahedral/cuboidal shape of the compositionally separated domains. The coalescence of such nanostructures along 〈004〉 directions gives rise to a rod-like morphology. The proposed model is expected to lead to a paradigm shift in the current understanding of CB-like nanostructures.

Identification of a coherent twin relationship from high-resolution reciprocal-space maps.

Twinning is a common crystallographic phenomenon which is related to the formation and coexistence of several orientation variants of the same crystal structure. It may occur during symmetry-lowering phase transitions or during the crystal growth itself. Once formed, twin domains play an important role in defining physical properties: for example, they underpin the giant piezoelectric effect in ferroelectrics, superelasticity in ferroelastics and the shape-memory effect in martensitic alloys. Regrettably, there is still a lack of experimental methods for the characterization of twin domain patterns. Here, a theoretical framework and algorithm are presented for the recognition of ferroelastic domains, as well as the identification of the coherent twin relationship using high-resolution reciprocal-space mapping of X-ray diffraction intensity around split Bragg peaks. Specifically, the geometrical theory of twinned ferroelastic crystals [Fousek & Janovec (1969). J. Appl. Phys. 40, 135-142] is adapted for the analysis of the X-ray diffraction patterns. The necessary equations are derived and an algorithm is outlined for the calculation of the separation between the Bragg peaks, diffracted from possible coherent twin domains, connected to one another via a mismatch-free interface. It is demonstrated that such separation is always perpendicular to the planar interface between mechanically matched domains. For illustration purposes, the analysis is presented of the separation between the peaks diffracted from tetragonal and rhombohedral domains in the high-resolution reciprocal-space maps of BaTiO3 and PbZr1-xTixO3 crystals. The demonstrated method can be used to analyse the response of multi-domain patterns to external perturbations such as electric field, change of temperature or pressure.

Revealing intrinsic electro-optic effect in single domain Pb(Zr, Ti)O3 thin films

We deposited polar-axis-oriented tetragonal and rhombohedral single domain Pb(Zr, Ti)O3 (PZT) films on CaF2(100) substrates by inserting SrRuO3 (SRO)/LaNiO3 and SRO/SrTiO3/TiO2/CeO2 buffer layers. Both PZT films grew epitaxially and had a (001)- and (111)-domain with the remnant polarization and piezoelectric constant comparable to the theoretical values of PZT single crystals having the same compositions. The electro-optic (EO) response of the fabricated PZT films was constant with respect to the DC electric field and increased linearly with an increasing AC electric field, thus representing a typical linear EO response in single domain ferroelectrics. The measured EO coefficients were larger than the value for a single crystal of PbTiO3, i.e., one of the end members of PZT, but smaller than the values reported for polycrystalline and epitaxial PZT films with multiple domains. These findings show that the intrinsic EO effect is enhanced in PZT, which is similar to the enhancement seen in the dielectric and piezoelectric constants. Moreover, most of the reported EO response in PZT films is supported by additional extrinsic contributions.

Structural Insights of Electrical Aging in PZT Thin Films as Revealed by In Situ Biasing X-ray Diffraction.

Electrical aging in lead zirconate titanate (PbZrxTi1−xO3) thin films has been intensively studied from a macroscopic perspective. However, structural origins and consequences of such degradation are less documented. In this study, we have used synchrotron radiation to evaluate the behavior of ferroelectric domains by X-ray diffraction (XRD). The sample was loaded with an AC triangular bias waveform between ±10 V with a number of cycle varying from one up to 108. At each step of the aging procedure, XRD spectra had been collected in situ during the application of an electric field on a capacitor. The fine analysis of the (200) pseudo-cubic peak structure allows to separate the evolution of the volume of a/c tetragonal and rhombohedral domains along the electrical biasing. Throughout the aging, both intrinsic and extrinsic responses of tetra and rhombohedral domains are altered, the behavior depending on the observed phase. This methodology opens up new perspectives in the comprehension of the aging effect in ferroelectric thin film.

Improvement of magnetostriction performance by doping Mg in spinel MnV2O4

By a combination of magnetization M(T), M(H) and strain ΔL/L700K, ΔL/L0Oe, the positive magnetostrictions up to ∼5000 ppm originating from the rearrangement of tetragonal domains were observed in spinel Mn0.85Mg0.15V2O4, which exhibits two successive magnetic transitions at TC ∼ 42 K and T* ∼ 28 K. An anomalous magnetic hysteresis loop under a high field occurs below T*, caused by the rearrangement of tetragonal domains. We found that the Mg-doping at the Mn site can effectively promote the positive magnetostriction in Mn1-xMgxV2O4 systems. Moreover, the remnant strain can be significantly lowered by Mg-doping due to the enhancement of magnetic anisotropy. These results provide a possible approach for further optimizing the performance of magnetic shape-memory materials.

Role of tetragonal distortion on domain switching and lattice strain of piezoelectrics by in-situ synchrotron diffraction

The tetragonal phase is an indispensable component that plays an important role in forming the morphotropic phase boundary. Herein, the piezoelectric behaviors are systematically investigated in various Pb/Bi-based tetragonal piezoelectric systems as a function of tetragonal distortion using in-situ high-energy synchrotron diffraction. It is found that the tetragonal distortion has a significant influence on piezoelectric properties through constraining the domain switching. Specifically, a critical value of (c/a-1) ≈ 1.5 % is identified, below which the domain switching is significantly activated. The correlation between piezoelectric performance and the cooperative contribution of tetragonal distortion and domain switching has been established: Reducing tetragonal distortion and activating domain switching can enhance the piezoelectric coefficient. Furthermore, an approximate linear coupling between domain switching and lattice strain is confirmed in tetragonal piezoelectric systems. Insights from this work would facilitate the design of high-performance piezoelectrics, by controlling tetragonal distortion and domain switching.

Domain Control by Adjusting Anisotropic Stress in Pyrochlore Oxide Cd2Re2O7

The 5d pyrochlore oxide Cd2Re2O7 exhibits successive phase transitions from a cubic pyrochlore structure (phase I) to a tetragonal structure without inversion symmetry below Ts1 of ~200 K (phase II) and further to another noncentrosymmetric tetragonal structure below Ts2 of ~120 K (phase III). The two low-temperature phases may be characterized by odd-parity multipolar orders induced by the Fermi liquid instability of the spin-orbit-coupled metal. To control the tetragonal domains generated by the transitions and to obtain a single-domain crystal for the measurements of anisotropic properties, we prepared single crystals with the (0 0 1) surface and applied biaxial and uniaxial stresses along the plane. Polarizing optical microscopy observations revealed that inducing a small strain of approximately 0.05% could flip the twin domains ferroelastically in a reversible fashion at low temperatures, which evidences that the tetragonal deformation switches at Ts2 between c > a for phase II and c < a for phase III. Resistivity measurements using single-domain crystals under uniaxial stress showed that the anisotropy was maximum at around Ts2 and turned over across Ts2: resistivity along the c axis is larger (smaller) than that along the a axis by ~25% for phase II (III) at around Ts2. These large anisotropies probably originate from spin-dependent scattering in the spin-split Fermi surfaces of the cluster electric toroidal quadrupolar phases of Cd2Re2O7.

Unusual magnetostriction behavior and magnetoelectric effect in spinel MnV2O4

We investigated the magnetostriction behaviors and magnetoelectric effect of spinel structured $\mathrm{Mn}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$ using the magnetization, thermal expansion, magnetostriction, permittivity, and pyroelectricity measurements. Two successive transitions were observed at ${T}_{S}$ and ${T}^{*}$ in all measurements. The weak electric polarization begins to appear below ${T}_{S}$, and can be suppressed noticeably by applying a magnetic field below ${T}^{*}$, indicative of the obvious magnetoelectric effect in $\mathrm{Mn}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$. Furthermore, $\mathrm{Mn}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$ exhibits large low-field magnetostriction up to 6000 ppm at 7 kOe between ${T}^{*}$ and ${T}_{S}$. Except for the strain at the structural transition ${T}_{S}, \mathrm{Mn}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$ also shows another large strain at ${T}^{*}$ under the magnetic field, originating from the rearrangement of tetragonal domains. Decreasing temperature allows the easy magnetization axis of $\mathrm{Mn}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$ to rotate from parallel to the $a{b}_{\mathrm{T}}$ plane to parallel to the ${c}_{T}$ axis because of the disappearance of weak orbital fluctuations at ${T}^{*}$, which leads to the rearrangement of tetragonal domains at ${T}^{*}$ under the magnetic field.

Local Disorder at the Phase Transition Interrupts Ambipolar Charge Carrier Transport in Large Crystal Methylammonium Lead Iodide Thin Films

The low-temperature transition from a tetragonal to an orthorhombic crystal phase in methylammonium lead iodide (MAPI) is accompanied by drastic changes in the charge carrier mobility around a critical temperature of approximately 164 K. This transition is studied here using photoluminescence (PL) microscopy on large crystal MAPI thin films, which is extremely sensitive to modifications of the charge carrier dynamics and can resolve physical properties on a single-grain level. The key observation is that ambipolar charge carrier diffusion suddenly stops when the temperature falls below the phase transition temperature. From coexisting PL bands and their spatial distribution, it is concluded that the temperature range from just below the phase transition until about 150 K is determined by a mixed phase where small orthorhombic and tetragonal domains coexist. This results in local disorder, which hinders ambipolar charge carrier diffusion.